\newproblem{lay:1_1_4}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 1.1.4}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  Find the point of intersection of the lines $x_1+2x_2=-13$ and $3x_1-2x_2=1$
}{
   % Solution
	Let us construct the augmented system matrix
	\begin{center}
		$\left(\begin{array}{rr|r}
		   1 & 2 & -13 \\
			 3 & -2 & 1
		\end{array}\right)$
	\end{center}
	Now, we apply row operations to solve it
	\begin{center}
		\begin{tabular}{cc}
			 $\mathbf{r}_2\leftarrow \mathbf{r}_2-3\mathbf{r}_1$ &
				$\left(\begin{array}{rr|r}
					 1 & -5 & 1 \\
					 0 & -8 & 40
				\end{array}\right)$ \\
			 $\mathbf{r}_2\leftarrow -\frac{1}{8}\mathbf{r}_2$ &
				$\left(\begin{array}{rr|r}
					 1 & -5 & 1 \\
					 0 & 1 & -5
				\end{array}\right)$ \\
			 $\mathbf{r}_1\leftarrow \mathbf{r}_1+5\mathbf{r}_2$ &
				$\left(\begin{array}{rr|r}
					 1 & 0 & -3 \\
					 0 & 1 & -5
				\end{array}\right)$ \\
		\end{tabular}
	\end{center}
  The two lines intersect in a single point $(x_1,x_2)=(-3,-5)$.
	\begin{center}
		\includegraphics[scale=0.7]{Tema2/lay_1_1_4.eps}
	\end{center}
}
\useproblem{lay:1_1_4}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
